Some micro-electromechanical systems (“MEMS” or “MEMS devices”) can be used to detect motion, such as acceleration (e.g., an accelerometer) or rotation (e.g., a gyroscope). Some MEMS devices may include a mass (or “beam”) that is movable relative to another portion of the MEMS device (e.g., a substrate), and will displace in response to a motion. The motion of the MEMS device can be detected by a change in capacitance of one or more capacitors within the MEMS device, where the capacitance varies as a function of the displacement of the beam. For example, the beam may be suspended over an electrode on the substrate, and the beam and substrate electrode may form a capacitor, such that a change in that capacitance may be used to detect a change in the gap between the beam and substrate electrode.
Some MEMS devices employ one or more differential capacitors to detect displacement of a movable mass. A differential capacitor includes at least two electrodes. Specifically, one electrode is in a fixed position relative to the substrate or other part of the MEMS devices, while a movable electrode is part of, and moves with, the beam. The capacitor is defined, in part, by the gap between its fixed electrode and the movable electrode.
In one type of micromachined device, a beam is suspended over a substrate by supporting tethers (see e.g. U.S. Pat. No. 6,223,598). The supporting tethers act as springs, allowing the movable mass to move laterally relative to the substrate along an axis when the MEMS device is subject to the external force/acceleration. The supporting tethers also apply a restorative force counter to the external force, which normally pulls the beam back towards its nominal position. In normal operation, the displacement is small and the spring force of the tethers will restore the beam to its nominal, centered position.
The beam may be elongated along an axis, and may have a number of fingers that extend away from the beam in a direction perpendicular to the elongated axis of the beam and parallel to the substrate. The beam and fingers may displace laterally relative to the substrate along the axis, in response to an acceleration along the axis. Each of these movable fingers may be positioned between two fingers that are in the plane of the mass and are fixed relative to the substrate or some other part of the MEMS device. Each movable finger is an electrode, and each fixed finger is an electrode, and together a movable finger and a fixed finger form a capacitor. Together, the three electrodes form a differential capacitor cell.
In response to an external force/acceleration along a sensitive axis, the beam with a movable finger moves toward one or the other of the fixed fingers. The capacitance of the individual capacitors will change according to the displacement of the movable finger.
A variety of approaches can be used to sense the displacement of the beam with such a differential capacitor. Several approaches are described, for example, in U.S. Pat. No. 5,345,824.
In one type of prior art accelerometer, for example, the two fixed fingers in a differential capacitor are driven with AC carrier signals, such as sinusoids or square waves, that are preferably 180 degrees out of phase with respect to each other. If the beam is not displaced from its nominal position, no signal will be induced on the beam from the signals on the fixed fingers. However, if the beam has been displaced from its nominal position, for example by an acceleration, the change in the capacitances discussed above will cause a signal from the fixed electrodes to appear on the beam. The amplitude of the signal on the beam will be a function of the capacitances (e.g., a function of the gap between the movable electrode on the beam and the stationary finger electrodes), and the phase of that signal will be the phase of the periodic signal on the nearest fixed electrode. Thus the signal appearing on the beam may be processed to determine the displacement of the beam. This type of accelerometer may be known as an “open loop” accelerometer.
The signal on the beam may be demodulated in a variety of ways. One way of demodulating the signal on the beam is the use of a switched-capacitor demodulator.
Another type of accelerometer employs feedback. An accelerometer using this technique may be known as closed-loop, or force-feedback, or force-balanced accelerometer. In a force-balanced accelerometer, the output voltage of the accelerometer is fed back to the beam to counteract the displacement induced by acceleration. That feedback voltage represents the acceleration of the MEMS device.
As with the open-loop accelerometer, a finger on the beam is centered between two fixed fingers. In the force-balanced accelerometer, the two fixed fingers are at different DC potentials and are driven with AC carrier signals that are preferably 180 degrees out of phase with respect to each other. A DC offset is applied to the beam, resulting in a voltage difference between the beam and each of the fixed fingers. The DC offset is preferably centered between the DC potential of the two fixed fingers.
The voltage difference between the movable finger and a fixed finger results in an electrostatic force that may pull the two fingers towards each other. The attractive electrostatic force is generally described by the following equation:Force=εAV2/2d2 where:                (i) ε is the permittivity of the space between the plates, and is a physical constant depending on the material between the fingers;        (ii) A is the surface area of the fingers;        (iii) V is the voltage difference between the fingers; and        (iv) d is the distance between the fingers.This foregoing equation is accurate for a parallel plate capacitor, and is approximately correct for the finger-type capacitors described herein. The electrostatic force is attractive and proportional to the square of the voltage difference between the fingers, and inversely proportional to the square of the distance between the fingers. As the gap between fingers is reduced, the electrostatic force increases. Accordingly, the electrostatic force is nonlinear with displacement.        
The beam in an accelerometer such as those discussed above is subject to a number of forces. Under acceleration, a force will act to displace the beam according to Newton's law: F=MA. Countering this force is the spring force of the tethers, each of which acts to re-center the mass. The spring force is a function of the spring constant (K), and the displacement of the mass (X): F=KX (which may be known as Hooke's law). In addition, the two fixed electrodes will apply electrostatic forces to the beam, but in opposing directions.
As an example, if (1) the potential of the beam of an accelerometer as described above is established, and (2) the potential of one fixed finger is above the potential of the beam, and (3) the potential of the other fixed finger is an equal amount below the beam, then the two electrostatic attractive forces will balance each other when the beam is centered, i.e., in its nominal position. However, when the beam is displaced, the distance from the beam to one of the fixed fingers is reduced, causing an increase in the electrostatic force attracting that fixed finger and the beam. Conversely, the distance between the beam and the other fixed finger is increased, resulting in a reduction in the electrostatic force attracting them.
In normal operation, the force of the tethers is sufficient to return the beam to its nominal position once the acceleration force is removed, because the net electrostatic force is smaller than the spring force.
Under acceleration, the feedback loop (of the noted device using feedback) adjusts the feedback voltage to decrease the bias voltage on the nearest electrode, while increasing the bias voltage on the farthest fixed electrode, to supplement the restorative spring force in opposing the force of the acceleration. The signal at the output terminal is a measure of the force required to re-center the beam, and is therefore proportional to acceleration.
Thus, in the force-balance arrangement, the differential capacitors serve two purposes. First, they allow the displacement of the beam to be measured via the differential capacitance. Second, they apply electrostatic forces to balance the beam.
In both the open-loop and force-balanced devices, there is a potential difference between the beam and one or more fixed fingers, and that difference can become problematic in some circumstances.
In normal operation, the inventors have determined that with a given open loop accelerometer, for example, the displacement of the beam will cause a change in capacitance on the order of one percent to ten percent at full scale. In closed-loop operation, the change is less. Accordingly, the motion of the beam in normal operation is within a predictable range. However, a large acceleration or physical shock may displace the beam more than in nominal operation. Such a displacement means that one of the gaps in the differential capacitor is significantly reduced. As shown in the electrostatic force equation (above), the electrostatic force is non-linear with distance. As the gap is reduced, the force increases. At some point, the force of the electrostatic attraction may exceed the forces acting to return the beam to its nominal position. In that case, the beam may continue moving until the electrostatic force is so great that the beam is captured by, and may even come into contact with, the opposing fixed finger, and cannot return to its normal operating position. This situation is known in the art as “electrostatic capture.”
In the prior art, one way to prevent electrostatic capture is by using mechanical stoppers that physically limit the displacement of the beam. However, such a device must have a capacitor gap large enough to accommodate a stopper, and such a gap reduces the sensitivity of the device and degrades signal to noise ratio. Another approach would be to use lower voltages on the members, but that would also reduce the sensitivity of the device and degrade signal to noise ratio.
Alternately, electrostatic capture can be avoided or released by turning off power to the MEMS device completely, thus negating the voltage differential that is powering the electrostatic capture. However, this requires shutting down power to the MEMS device, which may be undesirable.